This work considers signatures that can express domain restriction of functions \(\circ \) . As already noted, Leech showed in [1]} that the functional algebras of signature \((\circ ,\sqcup )\) , or equivalently \((\circ ,\sqcup ,\diamond )\) , are finitely axiomatised as the variety of right handed strongly distributive skew lattices. However, despite the fact that the concept of a prime filter as in Subsection REF  makes sense in this setting, our representation method as in Proposition REF  does not seem to represent \(\sqcup \)  correctly when \({\mathcal {F}}\)  is chosen to be the prime filters. Hence the extended version of this signature in which composition is present remains unaxiomatised.
